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Consider a block of conducting material ...

Consider a block of conducting material of resistivity p shown in the figure. Current I enters at A and leaves from D. We apply superposition principle to find voltage `Delta v` developed between B and C. The calculation is done in the following steps :

(i) Take current I entering from A and assume it to spread over a hemispherical surface in the block.
(ii) Calculate filed E(r) at distance r from A by using Ohm’s law `E=pi` where j is the current per unit area at r.
(iii) From the r dependence of E(r), obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current I leaving D and superpose result for A and D.
`Delta v`measured between B and C is :

A

`(rhol)/(pi a)-(rhol)/(pi(a+b))`

B

`(rhol)/(a)-(rhol)/((a+b))`

C

`(rhol)/(2pia)-(rhol)/(2pi(a+b))`

D

`-(rhol)/(2pi(a-b))`

Text Solution

Verified by Experts

The correct Answer is:
C
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